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## Do this question looks familiar? (a kernel of a modulo over a group ring) [closed]

Let $G$ a finite $2$-group. Consider the Group Ring $F_2[G]$ over the field $F_2$ of two elements. Consider the matrix $M$ with $M_{i,j}=p_{i,j}$ for some $p_{i,j}\in F_2[G]$, $i=1,\cdots k$, $j=1,\cdots n$.

Let $V$ be the sub-$F_2[G]$-module of $\oplus^n F_2[G]$ generated by $\langle P_1,\cdots,P_k\rangle$ with $P_i=(p_{i,1},\cdots,p_{i,n})$ for $i=1,\cdots k$.

I am interested in the kernel of the transformation

$$M:V^n\to V^k.$$

T

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What is your question? I assume you're not actually asking if this question looks familiar, as your title suggests. There's probably something you want to know about the kernel of M, but you haven't said what it is, and you haven't provided any motivation, so it's hard to even guess what you're actually trying to accomplish. As is, I would vote to close this as not a real question. Please have a look at mathoverflow.net/howtoask for some tips on how to improve the question. – Anton Geraschenko Mar 25 2010 at 19:45